Translating Mathematical Phrases

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Translating Mathematical Phrases
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Question

• What does it mean to translate something?
  Explain in your own words on a sheet of paper.
  Be prepared to share your answer

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Can you translate these words (or phrases)?

• ROTFL
• lt3
• CYAL8R
• IMO
• NE1
• MYOB
• 5

• 2EZ
• L8R
• AFK
• BTW
• NVM
• ORLY
• TMI
• TTYL

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Question?

• Why were you able to (or unable to) translate the
  SMS words and phrases on the previous slide?

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Can you translate?

• What if you had additional info?

• ... . . / - .... .. ... / .. ... / -. --- - /
  ... --- / -... .- -.. .-.-.-
• -.-- --- ..- / .--- ..- ... - / -. . . -.. . -..
  / - .... . / -.-. --- -.. . / - --- / - .-. .- -.
  ... .-.. .- - . .-.-.-

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Question?

• Why were you unable to decode the messages on the
  previous slide at first?

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Math

• Mathematical language is no different than SMS
  messages or morse code.
• You have to learn the alphabet, vocabulary, and
  structure of the language before you can be
  fluent.

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Types of Math Language

• There are four main types of Math Language
• Expressions
• Equations
• Inequalities
• Word Problems

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The Alphabet Code Words and Operations
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It all starts with expressions

• Expressions are open ended thoughts.
• Things that are blurted out without necessarily
  creating a complete sentence
• Examples Hello Goodbye Watch out

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Mathematical Expressions

• Mathematical expressions are also open ended
  thoughts
• This means they lack the closure of an equal sign
• Lots of numbers may satisfy some expressions,
  which often leads to the use of a variable
• Variable Clues some number, a number, any
  number

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Try to translate the following

• Twelve more than a number.
• 5 less than a number.
• 3 times a number .
• A number divided by 12

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Lets try some harder expressions

• The square of k decreased by 7
• Four times 2 plus 7
• 5 times the sum of a number and 2
• A number divided into 5 equal parts

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Again

• The difference of -4 and a number decreased by
  ten
• 14 more than twice a number g
• Three-fifths of r cubed
• Triple the sum of 19 and a number minus the
  product of that same number and 6.

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Translating Equations

• Equations
• Equations are the step up from an expression.
• In an equation, a complete mathematical thought
  is presented that leads to just one answer.
• Much like a sentence, this complete thought
  requires punctuation
• An equal sign is used in an equation to complete
  the mathematical sentence and direct you to your
  answer.

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What to look for?

• When translating an equation
• You need to be aware of an additional set of
  code words that tell you to use the equal sign
• The main word to look for is the word IS
• Practice reading a simple number sentence and you
  will notice the natural tendency to say the word
  IS in place of the equal sign
• 4 3 7
• Four plus three IS seven

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Additional Code Words

• Some of the other code words that tell you to use
  an equal sign include
• Are
• Was
• Were
• Will Be
• Gives
• Yields
• Sold For

And of course EQUALS!
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Practice

• Translate each of these equations into a
  sentence.
• 8 6 2
• -5 34 29
• 45/5 9
• -3 4 -12

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What about this one?

• Translate the sentence into an algebraic
  equation.
• The number of girls in the class plus the number
  of boys in the class equals the number of
  students in the class
• What makes this problem more challenging?

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Now you try on your own

• Translate each problem into an algebraic equation
  and then solve that equation.
• Five more than a number is eight.
• Two times a number is ten.

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• Six less than a number is twenty-four.
• A number divided by five is ten.
• The sum of nine and a number is fourteen.

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• Nine subtracted from the quotient of a number and
  three is twenty-one.
• The difference of seven and three times a number
  is ten.
• One-half of a number added to seven is eleven.

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• Two less than the quotient of a number and five
  is one.
• The product of three and the sum of number and
  two is zero.

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Christmas Carol Assignment

• You are going to write your own version of the 12
  days of Christmas using equations to replace the
  numbers in the original song.
• Example On the first day of Christmas, my true
  love gave to me x 5 -4 partridges in a pear
  tree
• X would equal 1 and the first day of Christmas
  has one gift in the carol.

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Conditions

• You must write an equation for each of the 12
  days and the answer to the equation must match
  that day of Christmas
• You may change the my true love gave to me part
  to anyone that you would like to receive gifts
  from
• You may change the names of the gifts to anything
  school appropriate that you would like to receive

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Requirements

• Your equations must equal the correct number for
  the day.
• You will present your final carol on a sheet of
  the large construction paper (front only). Be
  sure to give yourself space. You DO NOT have to
  repeat the previous days as you advance.
• You must decorate your carol on the final copy
  with pictures (to represent the gifts) and
  colored outlining.

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Equation Requirements

• In your 12 days equations you must include
• An equation that uses a square root
• An equation that uses squaring a number
• An equation that uses parenthesis
• At least 3 two step equations
• A minimum of two equations for each of the four
  main operations (, -, x, )
• At least 3 equations that use negative numbers